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378 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
This form of definition of stability derivatives invoMng time derivatives such as
av, p, and angular velocity components P, q, r is necessary to make these deriva-
tives nondimensional like all the other stability and control der:ivatives. Further-
more, the nondimensionalization helps us use the results obtained on scaled model
tests in wind tunnels for predicting the stability and response of the full-scale
airplane.ln view of this,itis important to note ffiat C,nq + acm/aq ~d so on.
The stability and control derivarives with respect to variables such as ci, and p
are called acceleration derivatives, and those with respect to p, q, and r are called
rotary derivatives. Together, they are called dynamic stability-control derivatives.
Using short-hand notation, we can rewrite the expressions for forces and mo-
ments in the nondimensional form as follows:
ACx = CruU + Cxcr A2 + Cr0AO + C., (~U ) + C^q (2qU )
+ Cx8t A8e + Cxat A8r + - - . (4.41 1)
ACy = Cyp Ap + Cy+A4 + C,B (~fjb) + Cyp (2pf;.) + Cyr (23 )
+ Cy&i A8a + Cy8r A8r + . - . (4.412)
ACz = Cz,,u + Czcr Aa + Cza AO + Cz, Gu ) + Czq (2qU )
+ Cz8e A8e + Cz8,A8r + * *. (4.413)
AC, = C,tr Ap + C,a c~ejb) + Ct*A4 + CrP (2pUb ) + C,, (2t; )
+ Cl8a A8a + CIBr A8r + . . . (4.414)
AC,n : Cm,,u + Cmr Aa + C,,,o AO + C, , (~U ) + C"q (2qU )
+ Cm8e A8e + Cm& A8r + . . . (4.415)
ACn = Cnp A8 + C.B (jljb) + Cn~A~ + Cnp (2pUb ) + Cnr (2;;.)
+ Cnaa A8a + C,,tr Ab'r + . - . (4.416)
Itisinteresting to observe that, with the assumption of small distwrbances andlin-
ear uncoupled aerodynamics, Eqs. (4.393), (4.395), and (4.397) with Eqs. (4.411),
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